The innovative information-based framework for credit risk modeling, proposed recently by Brody, Hughston, and Macrina, is extended to a more general and practically important setup of random interest rates. We first introduce the market model, and we derive an explicit expression for...

Forward start options are examined in Heston's (Review of Financial Studies 6 (1993) 327–343) stochastic volatility model with the CIR (Econometrica 53 (1985) 385–408) stochastic interest rates. The instantaneous volatility and the instantaneous short rate are assumed to be correlated with...

The paper provides simple and rigorous, albeit fairly general, derivations of valuation formulae for credit default swaptions and credit default index swaptions. Results of this work cover as special cases the pricing formulae derived previously by Jamshidian [Finance and Stochastics 8 (2004)...

The optimal smoothed linear estimate in the Kalman-Bucy model is found by the direct minimization method.

The backward induction approach is systematically used to produce various models of forward market rates. These include the lognormal model of forward Libor rates examined by Miltersen et al. and Brace et al., as well as the lognormal model of (fixed-maturity) forward swap rates, which was...

This paper is the first in a series that we devote to studying the problems of valuation and hedging of defaultable game options in general, and convertible corporate bonds in particular. Here, we present mathematical foundations for our overall study. Specifically, we provide several results...

Properties of conditional expectations and metric projections for multivariate symmetric [alpha]-stable random variables with 1 < [alpha] < 2 are studied.

We study the pathwise uniqueness of solutions of one-dimensional stochastic differential equations involving local times, under the assumption that the diffusion coefficient satisfies the (LT) condition introduced by Barlow and Perkins (1984). We show that this condition is sufficient for the...

We examine the asymptotic behaviour of the call price surface and the associated Black-Scholes implied volatility surface in the small time to expiry limit under the condition of no arbitrage. In the final section, we examine a related question of existence of a market model with non-convergent...

The goal of this work is to examine the PDE approach to the valuation and hedging of defaultable claims in a Markovian model of credit risk. Our approach is based on the previous work by Bielecki et al. [3]. We extend the results in [3] by considering a general credit risk model, in which the...